Testing the significance of crossover receiver operating characteristic curves in the presence of multiple markers

In multivariate receiver operating characteristic (MROC) curve analysis, comparing two tests is usually done by means of area under the curve (AUC’s) and sensitivities. However, the existing procedures have not addressed the issue of comparing two MROC curves when they cross each other.
Methods & Materials: A modified version of AUC (mAUC) under MROC setup is proposed to address the above-mentioned problem. It is also shown that mAUC performs better than AUC. The performance of mAUC in the aspect of crossover curves is supported by a real dataset and simulation studies at different sample sizes.
Two real datasets, namely, Intra Uterine Growth Restricted Fetal Doppler Study (IUGRFDS) and Indian liver patient (ILP) datasets are used and apart from these simulation studies are also carried out to observe the effect of sample size. These mAUC’s are then compared with each other to show that difference exists between two curves while comparing AUC’s cannot identify the true difference existing between them. With respect to IUGRFDS dataset, MROC curves of the diagnostic procedures middle cerebral artery and cerebroplacental ratio cross each other and are found to be similar when their AUC’s and mAUC’s are compared. In ILP dataset, the extent of correct classification achieved in the case of males is shown to be better than that of females when mAUC’s at 0.5 and 0.8 are compared.
It is observed that the mAUC’s are competent in identifying the true difference between the crossover MROC curves when the sample size is adequate, and the λ values are 0.5 and 0.8 but not 0.3.